Violin is a hard instrument to master but if you have other music instrument knowledge, you could probably do it. There are ton's of help sites to help you learn. Good ones too. Go for it !
Is it possible to teach yourself to play the violin? If you already play other instruments and have a background in music? Or is it impossible?
I play the violin and I think you could definitely teach yourself! You should purchase books that have some instruction inside. I used the All for Strings series when I began and it is good for beginners.
Impossible is possible itself! (i'm possible). You can teach yourself how to play any instrument. Whether you go to a class or have a teacher, still all depends on you. In my opinion, the best way to learn an instrument is to do it by yourself, make the most awful noises till you make it right. Constant practice, not giving up and pouring your soul into it, repeat and repeat. The only thing you must do is to follow basic instructions by the books or even PDF files or websites on the internet.
Good luck on your journey.
random passerby, I truly think that it's absolutely possible, but it would be much harder than if you would hire any teacher for that purpose, who would help you with professional tips and tricks about violin playing. If you would need a violin, you can visit this best beginner violins website, and choose whatever you need. They produce pretty reliable music instruments I gotta say.